When the cowl vents get plugged, and rain water backs up in the cowl area, the water enters through the air inlet in the cowl area. That water gets both into the blower motor and resistor pack. It's likely the blower motor bearings are rusted, so it will not turn. Most certainly the resistor pack that controls the blower motor speed is shorted out and bad.

The water will leak down on the passenger side to the electronics under the floor carpet. It's very common that the stereo amp connector plugs get wet. They will corrode and short out.

I'm sorry to say, I expect you will need to replace the blower motor, resistor pack, and likely the stereo amp and the connectors. The fuses that power the motor and radio/amp may be blown.